[amp_mcq option1=”Proportional to A” option2=”Proportional to A2″ option3=”Proportional to $$\\frac{1}{{{{\\text{A}}^2}}}$$” option4=”Independent of A” correct=”option2″]<\/p>\n
The correct answer is: B. Proportional to A2<\/strong><\/p>\n The total energy of a particle executing simple harmonic motion is given by the equation:<\/p>\n $$E = \\frac{1}{2}m\\omega^2A^2$$<\/p>\n where $m$ is the mass of the particle, $\\omega$ is the angular frequency of the motion, and $A$ is the amplitude of the motion.<\/p>\n The angular frequency of the motion is given by the equation:<\/p>\n $$\\omega = \\frac{2\\pi}{T}$$<\/p>\n where $T$ is the period of the motion.<\/p>\n The period of the motion is given by the equation:<\/p>\n $$T = \\frac{2\\pi}{\\sqrt{k\/m}}$$<\/p>\n where $k$ is the spring constant.<\/p>\n Therefore, the total energy of the particle is given by the equation:<\/p>\n $$E = \\frac{1}{2}m\\left(\\frac{2\\pi}{\\sqrt{k\/m}}\\right)^2A^2 = \\frac{4\\pi^2}{m}k A^2$$<\/p>\n Since $k$ is a constant, the total energy of the particle is proportional to the square of the amplitude of the motion.<\/p>\n","protected":false},"excerpt":{"rendered":" [amp_mcq option1=”Proportional to A” option2=”Proportional to A2″ option3=”Proportional to $$\\frac{1}{{{{\\text{A}}^2}}}$$” option4=”Independent of A” correct=”option2″]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[645],"tags":[],"class_list":["post-6769","post","type-post","status-publish","format-standard","hentry","category-applied-mechanics-and-graphic-statics","no-featured-image-padding"],"yoast_head":"\n